The median

- it is a statistical value which is usually located at the center of a given set of data that has been organized in the order of size or magnitude as illustrating, consider the set 14, 17, 9, 8, 20, 32, 18, 14.5, 13. While the data is ordered it will be 8, 9, 13, 14, 14.5, 17, 18, 20, 32

The middle number or median is 14.5

-  The significance of the median lies in the fact that it divides the data into two equivalent halves. The number of observations above and below the median is equal.

-   In order to find out the value of the median from grouped data. While data is grouped the median may be determined by utilizing the given methods.

 

i.  Graphical method by using the cumulative frequency curve or ogive

ii.  The formula

Illustration

Referring to the table which is given below; determine the median by using the methods above

IQ	No of resid	UCB	Cumulative Frequency
0 - 20	6	20	6
20 - 40	18	40	24
40 - 60	32	60	56
60 - 80	48	80	104
80 - 100	27	100	131
100 - 120	13	120	144
120 - 140	2	140	146

 

                              

Hence the position of the median is= (n + 1)/2

= (146 + 1)/2

ii. Computation

The formula utilized is

                                             

Whereas L = Lower class boundary of the class having the median

            N = No of observations

            Cfo= cfbm = Cumulative frequency of the class before that having the median

            F1 fmc = Frequency of the class having the median

 

                                        

= 60 + ((73.5 - 56)/48) * 20

= 60 + 7.29

= 67.29

Posted Date: 2/16/2013 6:05:54 AM | Location : United States

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